Problem $1$: Extended Kalman Filter

$[5$ pts$]$ Assume that a ground robot is navigating in a $2$D environment. Assume further that there

are two landmarks $l_i=[l_x^i,l_y^i]$ at known positions in the environment. At each time step, the

robot observes both landmarks with some sensor noise. You will formulate an Extended Kalman

Filter $($EKF$)$ estimator for this problem by answering the following parts.

$($a$)$ Suppose that the robot's states are $p_x$ and $p_y,$ representing the positions in $x-$ and $y-$axes,

respectively. The robot's control inputs are $v_x$ and $v_y,$ which are the velocities in $x-$ and

$y-$axes, respectively. Formally define the discrete$-$time dynamical model of the robot that

is subject to some Gaussian process noise. For each variable you define, specify its domain

$($e$.$g$.,$ if you define a matrix $M,$ indicate it as $Min{R}^{nn}.)$

$($b$)$ Formally define the observation model which consists of the Euclidean distances from the

robot's current position $(p_x,p_y)$ to each of the two landmarks for $($:$i=1,2$